Abstract
The Ginzburg-Landau model for superconductivity is considered in two dimensions. We show, for smooth bounded domains, that superconductivity remains concentrated near the surface when the applied magnetic field is decreased below H C3 as long as it is greater than H C2 . We demonstrate this result in the large-domain limit, i.e, when the domain's size tends to infinity. Additionally, we prove that for applied fields greater than H C2 , the only solution in ℝ2 satisfying normal-state conditions at infinity is the normal state. The above results have been proved in the past for the linear case. Here we prove them for non-linear problems.
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(Accepted May 7, 2002) Published online November 12, 2002
Communicated by D. KINDERLEHRER
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ALMOG, Y. Non-linear Surface Superconductivity for Type II Superconductors in the Large-Domain Limit. Arch. Rational Mech. Anal. 165, 271–293 (2002). https://doi.org/10.1007/s00205-002-0224-7
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DOI: https://doi.org/10.1007/s00205-002-0224-7